You have nothing to be worried about, nothing at all. Everyone's perception of going to have an STI test vary and, as I have read on here, seem to build on bad preconceptions and they are ill informed.
Every STI clinic should have a chaperone service, so you do not have to go through it alone, ask yours and find out whether they do this. The doctors and nurses are so understanding at the clinics and they will make you feel at ease.
I applaude you on going to get yourself checked out, only wish other people would do the same but in the end it all comes down to lack of education about STI's (you only have to read some of the topics on here) and bad preconceptions of check ups.
After you have gone you'll not know why you worried so much, trust me on this. You are doing the right thing.
Martin